A group of 25 particles have the following speeds: two have speed 11m/s , seven have 16m/s , four have 22m/s , three have 25m/s
1 answer:
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Answer:
a)
b) mg>N
c)
d)
Explanation:
In order to solve part a) of the problem, we can start by drawing a free body diagram of the presented situation. (see attached picture).
In this case, we know the centripetal acceleration is given by the following formula:
where:
we know the period of rotation of the earth is about 24 hours, so:
so we can now find the angular speed:
So the centripetal acceleration will be:
which yields:
b)
In order to answer part b, we must draw a free body diagram of us sitting on a chair. (See attached picture.)
So we can do a sum of forces in equilibrium:
so we get that:
and solve for the normal force:
In this case, we can clearly see that:
therefore mg>N
This is because the centripetal acceleration is pulling us upwards, that will make the magnitude of the normal force smaller than the product of the mass times the acceleration of gravity.
c)
So let's calculate our weight and normal force:
Let's say we weight a total of 60kg, so:
and let's calculate the normal force:
N=586.58N
so now we can calculate the percentage change:
so we get:
which is a really small change.
d) In order to find this acceleration, we need to start by calculating the radius of rotation at that point of earth. (See attached picture).
There, we can see that the radius can be found by using the cos function:
In this case:
so we can solve for r, so we get:
in this case we'll use the average radius of earch which is 6,371 km, so we get:
which yields:
r=4,551.91 km
and now we can calculate the acceleration at that point:
1. False
Explanation: it's exactly the opposite. In fact, Lenz's law states that the induced current and the induced emf in a conductor are generated in such a direction that opposes to the change in magnetic flux through the coil. This is summarized by the negative sign in the Faraday's Newmann Lenz law:
where is the emf induced and
is the rate of change of magnetic flux through the coil.
Lenz's law is a consequence of the law of conservation of energy. In fact, we have:
- If the magnetic flux through a coil is increasing, then the induced current has a direction such that the magnetic field generated by the coil is opposite to the direction of the external magnetic field, in order to decrease the total flux
- If the magnetic flux through a coil is decreasing, then the induced current has a direction such that the magnetic field generated by the coil is in the same direction as the external field, in order to increase the total flux
2. False
Explanation: the magnetic flux through a surface is given by
where
B is the magnitude of the magnetic field
A is the surface area
is the angle between the direction of B and the normal vector to the surface
As we see, the magnetic flux depends not only on B and A, but also on the orientation of the coil with respect to the magnetic field.
3. False
Explanation:
- Sound waves are mechanical waves: mechanical waves are waves consisting of oscillations of the particles in a medium. Due to their nature, therefore, mechanical waves can propagate only in the presence of a medium
- Electromagnetic waves are NOT mechanical waves: they consist of oscillations of electric and magnetic fields, in a direction perpendicular to the direction of propagation of the wave. Since em waves are not mechanical waves, they do NOT need a medium to propagate, since they can also travel through a vacuum; therefore the original statement is false.